Ygtjki

documentclass[12pt,reqno,a4paper]amsart
usepackageextsizes
usepackageblindtext
textheight 9.3in textwidth 6.5in
calclayout
usepackageamsmath,amsthm,amsfonts,amssymb
usepackagehyperref
usepackagemathrsfs
usepackage[all]xy
usepackage[normalem]ulem
usepackagetikz-cd
usepackage[utf8]inputenc
usepackage[english]babel
begindocument
[begintikzcd
underlineV 
arrow[rrrrdd, bend left]
arrow[rrdddd, bend right] arrow[rrdd, dotted] & && & \
& & & & \
& & A arrow[dd] arrow[rr] & & B arrow[dd] \
& & & & \
& & C arrow[rr] & & D 
endtikzcd]
enddocument

above code is giving me following diagram

I used "phantom" technique to number part of commutative diagram. It did not work. I want to write

• (1) in the diagram enclosed by V,A,B


• (2) in the diagram enclosed by V,A,C


• (3) in the diagram enclosed by A,B,C,D

Can some one help me to see how to do this?

Just for fun: tikz-cd is based on TikZ so

documentclass[tikz]standalone
begindocument
begintikzpicture[y=0.8cm]
node (a) at (0,0) $A$;
node (b) at (2,0) $B$;
node (c) at (0,-2) $C$;
node (d) at (2,-2) $D$;
node (v) at (-2,2) $underlineV$;
draw[->] (a)--(b);
draw[->] (b)--(d);
draw[->] (a)--(c);
draw[->] (c)--(d);
draw[dotted,->] (v)--(a);
draw[->] (v) to[bend right] (c);
draw[->] (v) to[bend left] (b);
node at (1,-1) (3);
node at (0,1) (1);
node at (-1,0) (2);
endtikzpicture
enddocument

Without code...

Is this what you mean?

You can add the labels to your diagram with no arrows:

[begintikzcd
underlineV 
arrow[rrrrdd, bend left]
arrow[rrdddd, bend right] arrow[rrdd, dotted] & && & \
& & (1) & & \
& (2) & A arrow[dd] arrow[rr] & & B arrow[dd] \
& & & (3) & \
& & C arrow[rr] & & D 
endtikzcd]

With phantom arrows:

documentclass[a4paper]article
usepackagetikz-cd

begindocument

[
begintikzcd[nodes in empty cells]
underlineV
 arrow[rrrrdd, bend left]
 arrow[rrdddd, bend right]
 arrow[rrdd, dotted]
 arrow[rrrrdd,phantom,"(1)" description]
 arrow[rrdddd,phantom,"(2)" description]
\
&&&&\
&& A arrow[dd] arrow[rr] & arrow[dd,phantom,"(3)" description] &
B arrow[dd] \
&&&&\
&& C arrow[rr] && D
endtikzcd
]

enddocument